In this paper we show that the space of spinors over a warped product over S~1 has a certain splitting ΓΣ=?W(k,n) in spaces of spinors of weight k and winding number n which is respected by the Dirac operator. The same holds for the space of functions and the Laplace operator. We give eigenvalue estimates for the eigenvalues λ_(k,n) of the Dirac operator with eigenspinors of weight k and winding number n and eigenvalues μ_(m,n) of the Laplace operator with eigenfunctions of weight m and winding number n. In particular, we show that μ_k~2,n ≥ λ_(k,n)~2 holds for large n on S~1 * f T~l where T~l is a flat torus with the trivial spin structure.
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机译：在本文中，我们证明了在S〜1上的扭曲产品上的旋转子空间在权重为k且绕组数为n的旋转子空间中具有一定的分裂ΣΣ=ΔW（k，n），这是狄拉克算子所遵循的。函数空间和Laplace运算符也是如此。我们给出Dirac算子的特征值λ_（k，n）的特征值λ_（k，n），其特征旋子的权重为k，绕组数为n;而Laplace算子的特征值μ_（m，n）的特征值μ_（m，n），特征函数为权重m，绕组数为n。特别地，我们表明μ_k〜2，n≥λ_（k，n）〜2在S〜1 * f T〜l上对于大n成立，其中T〜l是具有微不足道的自旋结构的扁平圆环。
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